Art. 167. PORTALS POSTS PARTIALLY FIXED. 333 



When x=a in (166), y=y lf 



^c-a). .(168) 

 El'y' l = (same as (168) with the letters primed) ____ (169) 

 Moments about Q=0 (Fig. 218). 



,e-^~ ( 170 > 



= y\ and H=R+P-H' (171) 



Combining (168) and (169), and substituting from (170) 

 and (171), 



^\2(R +P)a(2a -c) -JW 2 (5a -2c) +Mi(c -a)l +rl Mt'(5a' -2c') - Afi'(e' -a')l 



H'-li: ,4-^ - ! (172) 



When a=af, c=c', and 1=1' , 



Equation (123) becomes 





Jfefjss.JAjj/Xj and M 2 =^k 2 D 2 =Hx 1 (175) 



Mj' =\k^D^ and <M" 2 ' =^k 2 D 2 =H f x 1 f (176) 



It will be necessary to determine H and o^ for two cases, 

 one with the live load on the bridge and one with no live load 

 acting. 



D^DL or DL+LL (177) 



D^DL + V or DL+LL + V=D 2 ' (178) 



D 2 =DL-V or DL+LL-V (179) 



Since M 2 ' will be greater than M 2 , x/ will be greater than 

 EJ. We can find a value which will be nearly a mean of the two 

 by using equation (172) or (173) to find H f and neglecting V 

 in equations (175) and (176). We have then: 



Approx. mean value of x and x i = * g 



Since M l does not involve V it can be determined at once 

 from (175). Guessing at a value of F, an approximate value 

 of MJ for use in (174) is obtained which may be revised as 

 soon as 7 has been approximately determined. M/ can be 



